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Higher Order Convergence Rates in Theory of Homogenization: Equations of Non-divergence Form

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Abstract

We establish higher order convergence rates in the theory of periodic homogenization of both linear and fully nonlinear uniformly elliptic equations of non-divergence form. The rates are achieved by involving higher order correctors which fix the errors occurring both in the interior and on the boundary layer of our physical domain. The proof is based on a viscosity method and a new regularity theory which captures the stability of the correctors with respect to the shape of our limit profile.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Seoul National University, Seoul, 151-747, Korea

    Sunghan Kim & Ki-Ahm Lee

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  1. Sunghan Kim
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  2. Ki-Ahm Lee
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Correspondence to Sunghan Kim.

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Communicated by G. Del Maso

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Kim, S., Lee, KA. Higher Order Convergence Rates in Theory of Homogenization: Equations of Non-divergence Form. Arch Rational Mech Anal 219, 1273–1304 (2016). https://doi.org/10.1007/s00205-015-0921-7

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  • DOI: https://doi.org/10.1007/s00205-015-0921-7

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